414
420
621
620
Answer is Wrong!
Answer is Right!
The correct answer is (a) 414.
The arithmetic mean of a set of numbers is the sum of the numbers divided by the number of numbers. In this case, the arithmetic mean is 41, and there are 15 numbers. Therefore, the sum of the numbers is $41 \times 15 = 414$.
Option (b) is incorrect because it is the sum of 14 numbers, not 15 numbers. Option (c) is incorrect because it is the sum of 16 numbers, not 15 numbers. Option (d) is incorrect because it is the sum of 15 numbers that are all equal to 41, which is not a realistic scenario.